Problem: Rewrite as a simplified fraction. ${0.3\overline{2} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 32.2222...\\ 10x &= 3.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 29}$ ${x = \dfrac{29}{90}} $